The announcement that Birmingham prison is the first in the public sector to be privatised has opened another row between the government and unions.

The POA, the prison officers' union, said it has launched a judicial review into the G4S consultancy role carried out by Phil Wheatley, the former director general of the prison service, after Kenneth Clarke, the justice secretary, announced on Thursday that the private sector security company is to take over the running of the prison in October.

G4S was awarded the contract under a market testing process, which began under former Labour justice secretary Jack Straw, that allowed private companies to bid for four prison contracts alongside the public sector.

Colin Moses, national chair of the POA, said questions needed to be answered about Wheatley's role and his current position at G4S.

"We launched the review because we believe he was a main player in the lead up to this decision," Moses said. "He was director general of the prison service for a number of years before becoming chief executive of the National Offenders Management Service. He started [the market testing] process right at the beginning with Jack Straw and he leaves, and six months later he's working for G4S. We need to know the details of this."

"It was a political decision, not Phil Wheatley's decision, brought about by Jack Straw when he was justice secretary," said Paddy Scriven, general secretary of the PGA. "The prison service tried to bring a round of negotiations over proposals for workforce modernisation, which was mainly about staff grading, but the proposals they came up with weren't acceptable. For us, this wasn't about pay and money but that the proposals the prison service was wedded to wouldn't have offered safe prisons.

Scriven said Straw had used market testing "as a punishment" over a failure to accept prison workforce modernisation proposals as they stood.

Scriven added that Clarke had "gone about face" in picking up the former Labour government's policy.

Clarke also defended the decision to award G4S a contract to run a new-build "supersize" prison, housing 1,600 inmates, next to Featherstone prison in Wolverhampton in April 2012. While Serco, which runs Doncaster prison, a private sector build, will become the first prison to be run under the payment by results system and would work with volunteer organisations to deliver results, Clarke said.

All prisons in the UK have been told to deliver 10% efficiency savings over the next four years and Clarke said Birmingham, Rochdale and Doncaster would bring "culmulative savings" of £216m over their initial 14-year contracts.

But the PGA said the market testing process was "extraordinarily expensive" with the failed tender process in Birmingham costing £2m and taking two years to put together.

"We dislike market testing and in our view prisons should be the responsibility of the state," Scriven said. "If ministers want a way of reducing costs we should be looking at service agreements not market testing, which is extraordinarily expensive and disruptive.

"If you want to drive down costs then we think this can be done using a process of internal competition. Prisons are a duty of the state not to be run for profit."

Thirteen private prisons already exist in the UK, run by G4S, Serco and Kalyx, but none were initially run by the public sector.

Buckley Hall, a third prison in Rochdale that was under bids, will remain in the public sector.

In response to the POA's review, a G4S spokesman said that Wheatley had been entirely transparent and had no links to the bidding process.

"Phil Wheatley joined G4S as an associate on 1 January 2011 to provide our care and justice division with strategic advice around the development of its global offering. In line with the recommendations of the [government's] advisory committee on business appointments, Phil ensured that his association with G4S was discussed with and approved by the committee.

"At no time has Phil been involved in any part of the tendering process for the competition for the management of prisons in the UK."

David Taylor-Smith, chief executive of G4S, said: "We have an excellent track record in running prisons on behalf of the government, dating back nearly 20 years to when we became the first private company to run a prison with HMP Wolds in 1992."